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Zbl 1233.35090
Carl, S.
Existence and comparison results for noncoercive and nonmonotone multivalued elliptic problems. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 8, A, 1532-1546 (2006). ISSN 0362-546X

Summary: We consider noncoercive quasilinear elliptic inclusions under multivalued flux boundary conditions involving multifunctions of Clarke's generalized gradient. Our main goal is to provide existence and comparison results which are based on an appropriate generalization of the notions of subsolutions and supersolutions. Furthermore, compactness and extremality results of the solution set enclosed by an ordered pair of sub-supersolutions will be proved.

MSC 2000:: *35J60 Nonlinear elliptic equations
35R70 PDE with multivalued right-hand sides
47H04 Set-valued operators

Keywords: quasilinear elliptic inclusion; Clarke's generalized gradient; multivalued pseudomonotone operators; multivalued Neumann boundary condition; subsolution; supersolution; extremal solution; comparison; compactness

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